Solve the absolute value inequality.   |2-5x| < or equal to 0. (2 minus 5x is less than or equal to 0)

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kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

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| 2 - 5x | <= 0

the absolute value is always positive. Therefore, it is never less than zero. It can, however, be equal to zero:

2 - 5x = 0

x = 2/5

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve |2-5x| < = 0

Solution:

If 2-5x is < 0 then |2-5x| = 5x-2  by definition . So 5x-2 < 0 by definition.

It is a contradiction

If 2-5x > 0, then |2-5x| =2-5x by definition. So 2-5x < 0 a contradiction.

So x > 2/5.

2 < 5x, x >2/5.

So x cannot be greater than 2/5 and x cannot be less than 2/5.

Therefore x = 2/5 is the only value that satisfies |2-5x| < = 0.

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atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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|2-5x| < or equal to 0

the l  l makes the numbers positive so:

2 + 5x < or equal to 0

now move the 5x

2 `<=` -5x

divide by -5

`2/-5 >= x`

now change the sign since you divided:

`2/-5 lt=` `x`

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zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

|2-5x| < or equal to 0.

so 2-5x< or equal to 0

Move the 5x on the other side so the equation stays positive

2<5x

then simply divide by 5 to isolate the variable (x)

x>2/5 

The sign changed because you divided by 5, once you divide it changes the sign

So the answer is x>2/5

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